I can't tell from the picture why that cylinder is dry, pitted, and scratched, while the others aren't. Maybe a bad plug, causing a misfire, and the unburned gas washing the oil off the cylinder wall? That's the starter button. Normally, you turn the key, then press that button to start the tractor. Incorporates a neutral safety feature. This site sells many parts, including wiring harnesses. Usually, you don't need the exact year. The one I linked is for if your tractor is still a 6V system. There's another harness for a 12V system, and a 12V conversion kit, with a harness.